SP2Support WP 2.1Track bed quality assessment Task Numerical modelling of poor quality sites First phase report on the modelling of poor quality sites CZECH TECHNICAL UNIVERSITY IN PRAGUE

Numerical modelling: list of FE models List of the studied models: 1. axisymmetric FE model of the experimental box 2. 3-D FE model of the experimental box 3. axisymmetric FE model of the in-situ conditions 4. 3-D FE model with reinforcing geogrid

FE modelling of laboratory experiments 1.Why? To reduce number of experiments needed to evaluate all possible situations 2.Variable parameters (material properties, construction layer thickness, contact behaviour)‏ 3.To assess the importance of each variable observed (sensitivity analysis)‏ 4.Result: nomograms (e.g. layer thickness vs. bearing capacity required)‏

strain gauge rosettes from principal strains using correlation method with FE model calculate the vertical displacements very precise assessment of the deformation area validation of the numerical model Settlement of the rubber (soil) measured by strain gauges

Results for 22.5 tons 25.0 tons and 27.5 tons loading temperature compensation included good correspondence with theory deformation known in all points

FEM model of the experimental box with sleeper experimental box modelled vertical displacement in good correlation with the measured values known strains and stresses relationship between vertical displacement and principal strains

Results - vertical displacements calculated vs. measured - for all cases: B35/SB20/E20, B35/SB20/E20, B45/SB20/E20 - good correspondence with the experimental results for all cases (average standard deviation is 16.7 %), except for the case of ballast thickness 350 mm - discrepancy caused by an error in measurement of the sleeper deflections - calculated displacements at the ballast sub-ballast interface in good agreement with experimental values even in the case of ballast thickness 350 mm (average standard deviation less than 15.6 %)‏

Design graphs for single layer construction axisymmetrical, fully parametric FE models results in terms of design graphs horizontal axis = modulus of deformation of the existing subgrade vertical axis = sub-ballast thickness required to achieve specified modulus of deformation on the top

Example of the design graphs Required modulus of deformation Steps in 5 MPa increments

Design graphs for two layer construction again axisymmetrical, fully parametric FE models results in terms of design graphs thickness of the top layer held constant, design graphs for required modulus of deformation in

Design graphs for construction with geosynthetics again axisymmetrical, fully parametric FE models material properties of geosynthetics important proper modelling of the contact studied calibrated with the experimental measurements from the box

Extension of our parametric FE models to rail track plain strain and 3-D models quadratic elements used high quality of elements required proper contact modelling studied evaluation of design criteria assessed using parametric modelling

results as design graphs On-going work :: reinforcing effect of cement layer

Geogrids and geotextilies modelling in 3D 2-D and 3-D models importance of proper geogrid modelling proper contact behaviour modelling significance of different size of mesh contact behaviour and increase of bearing capacity verified by physical modelling in the experimental box

Probabilistic approach scatter of input parameters (material properties) described by e.g. Gaussian distribution with standard deviation of ±3 – 5% how large is the scatter of the output parameters (settlement, stress, etc)? which input variables contribute the most to the scatter of an output parameter and to the failure probability? what are the sensitivities of the output parameter with respect to the input variables? Monte-Carlo, Latin hypercube,